4,155 research outputs found
Optimal eigenvalues estimate for the Dirac operator on domains with boundary
We give a lower bound for the eigenvalues of the Dirac operator on a compact
domain of a Riemannian spin manifold under the \MIT bag boundary condition.
The limiting case is characterized by the existence of an imaginary Killing
spinor.Comment: 10 page
Rigidity of compact Riemannian spin Manifolds with Boundary
In this article, we prove new rigidity results for compact Riemannian spin
manifolds with boundary whose scalar curvature is bounded from below by a
non-positive constant. In particular, we obtain generalizations of a result of
Hang-Wang \cite{hangwang1} based on a conjecture of Schroeder and Strake
\cite{schroeder}.Comment: English version of "G\'eom\'etrie spinorielle extrins\`eque et
rigidit\'es", Corollary 6 in Section 3 added, to appear in Letters Math. Phy
4D visualization of embryonic, structural crystallization by single-pulse microscopy
In many physical and biological systems the transition from an amorphous to ordered native structure involves complex energy landscapes, and understanding such transformations requires not only their thermodynamics but also the structural dynamics during the process. Here, we extend our 4D visualization method with electron imaging to include the study of irreversible processes with a single pulse in the same ultrafast electron microscope (UEM) as used before in the single-electron mode for the study of reversible processes. With this augmentation, we report on the transformation of amorphous to crystalline structure with silicon as an example. A single heating pulse was used to initiate crystallization from the amorphous phase while a single packet of electrons imaged selectively in space the transformation as the structure continuously changes with time. From the evolution of crystallinity in real time and the changes in morphology, for nanosecond and femtosecond pulse heating, we describe two types of processes, one that occurs at early time and involves a nondiffusive motion and another that takes place on a longer time scale. Similar mechanisms of two distinct time scales may perhaps be important in biomolecular folding
Nanoscale Mechanical Drumming Visualized by 4D Electron Microscopy
With four-dimensional (4D) electron microscopy, we report in situ imaging of the mechanical drumming of a nanoscale material. The single crystal graphite film is found to exhibit global resonance motion that is fully reversible and follows the same evolution after each initiating stress pulse. At early times, the motion appears âchaoticâ showing the different mechanical modes present over the micron scale. At longer time, the motion of the thin film collapses into a well-defined fundamental frequency of 1.08 MHz, a behavior reminiscent of mode locking; the mechanical motion damps out after âŒ200 ÎŒs and the oscillation has a âcavityâ quality factor of 150. The resonance time is determined by the stiffness of the material, and for the 75 nm thick and 40 ÎŒm square specimen used here we determined Youngâs modulus to be 1.0 TPa for the in-plane stressâstrain profile. Because of its real-time dimension, this 4D microscopy should have applications in the study of these and other types of materials structures
Model for self-tuning the cosmological constant
The vanishing cosmological constant in the four dimensional space-time is
obtained in a 5D Randall-Sundrum model with a brane (B1) located at . The
matter fields can be located at the brane. For settling any vacuum energy
generated at the brane to zero, we need a three index antisymmetric tensor
field with a specific form for the Lagrangian. For the self-tuning
mechanism, the bulk cosmological constant should be negative.Comment: LaTeX file of 4 pages, to appear in Phys. Rev. Let
Ramond-Ramond Fields, Fractional Branes and Orbifold Differential K-Theory
We study D-branes and Ramond-Ramond fields on global orbifolds of Type II
string theory with vanishing H-flux using methods of equivariant K-theory and
K-homology. We illustrate how Bredon equivariant cohomology naturally realizes
stringy orbifold cohomology. We emphasize its role as the correct cohomological
tool which captures known features of the low-energy effective field theory,
and which provides new consistency conditions for fractional D-branes and
Ramond-Ramond fields on orbifolds. We use an equivariant Chern character from
equivariant K-theory to Bredon cohomology to define new Ramond-Ramond couplings
of D-branes which generalize previous examples. We propose a definition for
groups of differential characters associated to equivariant K-theory. We derive
a Dirac quantization rule for Ramond-Ramond fluxes, and study flat
Ramond-Ramond potentials on orbifolds.Comment: 46 pages; v2: typos correcte
Dimensionality, topology, energy, the cosmological constant, and signature change
Using the concept of real tunneling configurations (classical signature
change) and nucleation energy, we explore the consequences of an alternative
minimization procedure for the Euclidean action in multiple-dimensional quantum
cosmology. In both standard Hartle-Hawking type as well as Coleman type
wormhole-based approaches, it is suggested that the action should be minimized
among configurations of equal energy. In a simplified model, allowing for
arbitrary products of spheres as Euclidean solutions, the favoured space-time
dimension is 4, the global topology of spacelike slices being (hence predicting a universe of Kantowski-Sachs type). There is,
however, some freedom for a Kaluza-Klein scenario, in which case the observed
spacelike slices are . In this case, the internal space is a product
of two-spheres, and the total space-time dimension is 6, 8, 10 or 12.Comment: 34 pages, LaTeX, no figure
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